Finite Element Modeling of Magnetically-Damped Convection in Conducting Melts

"A fully 3-D, transient finite element model is developed to represent the magnetic damping effects on complex fluid flow, heat transfer and electromagnetic field distributions in a metallic melt. The model development is based on our in-house finite element code for the fluid flow, heat transfer and electromagnetic field calculations. The numerical model is tested against numerical and experimental results for water as reported in literature. Various numerical simulations are carried out for the melt convection and temperature distribution with and without the presence of a transverse magnetic field. Numerical results show that magnetic damping can be effectively applied to stabilize melt flow, reduce turbulence and flow levels in the melt and over a certain threshold value a higher magnetic field resulted in a greater reduction in velocity. Also, for the study of melt flow instability, a long enough running time is needed to ensure the final fluid flow recirculation pattern. Moreover, numerical results suggest that there seems to exist a threshold value of applied magnetic field, above which magnetic damping becomes possible and below which the convection in the melt is actually enhanced.1. INTRODUCTIONThe imposition of a DC magnetic field on a moving, electrically conducting fluid, such as molten metal or semiconductor melt, produces an opposing Lorentz force that results in a reduction of flow velocity in the liquid. This effect has been explored in both the semiconductor and metals industries to control natural convection and/or surface tension induced Marangoni convection as well as thermally induced flow instability during solidification processing of these melts [1-6]. A mathematical model can be of great use in developing both fundamental understanding of the fluid-magnetic field interactions in these magnetically-assisted processing systems and basic guidelines for process design, control and optimization.This paper presents a 3-D mathematical model for magnetically damped fluid flow and heat transfer in a melt cavity, which is useful for interpreting results for unidirectional solidification processes at slow solidification rate, and some preliminary results concerning the magnetic damping effects on the flow instability in the melt. The model development is based on the finite element solution of the Navier-Stokes equations, energy equations and equations for induced electric field. The model is tested against reported results and is then applied to study the fluid flow and thermal distribution in the metallic melt with and without an external magnetic field."